Conformal Data and Renormalization Group Flow in Critical Quantum Spin Chains Using Periodic Uniform Matrix Product...

Area of Science:

• Quantum Many-Body Physics
• Condensed Matter Theory
• High-Energy Physics

Background:

• Critical quantum spin chains exhibit universal behavior governed by conformal field theories (CFTs).
• Accurate numerical methods are crucial for studying these systems, especially for extracting critical exponents and scaling dimensions.

Purpose of the Study:

• To demonstrate that periodic uniform matrix product states (PUMPS) can accurately approximate low-energy eigenstates of critical quantum spin chains.
• To use PUMPS in conjunction with established CFT methods to identify scaling operators and extract conformal data.
• To investigate the nonperturbative renormalization group (RG) flow of spectral properties between different CFTs.

Main Methods:

• Application of the Bloch-state ansatz using periodic uniform matrix product states (PUMPS).
• Integration with the Koo-Saleur formula for mapping eigenstates to scaling operators.
• Numerical analysis of the quantum Ising model and a generalized version.

Main Results:

• PUMPS accurately approximate low-energy eigenstates of critical quantum spin chains.
• Precise extraction of conformal data, including scaling dimensions, from the low-energy spectrum.
• Nonperturbative investigation of RG flow between the tricritical Ising CFT and the Ising CFT, showing agreement with analytical conjectures.

Conclusions:

• The PUMPS Bloch-state ansatz is a powerful tool for studying critical quantum systems.
• This approach provides a numerically accurate method for extracting CFT data and studying RG flow.
• The findings offer new insights into the behavior of quantum spin chains at criticality.